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1. The L _p chord Minkowski problem

   https://doi.org/10.1515/ans-2022-0041  

   Xi, Dongmeng; Yang, Deane; Zhang, Gaoyong; Zhao, Yiming (January 2023, Advanced Nonlinear Studies)

   Abstract Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n {{\mathbb{R}}}^{n} , in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p {L}_{p} chord measures is called the L p {L}_{p} chord Minkowski problem in the L p {L}_{p} Brunn-Minkowski theory, which includes the L p {L}_{p} Minkowski problem as a special case. This article solves the L p {L}_{p} chord Minkowski problem when p > 1 p\gt 1 and the symmetric case of 0 < p < 1 0\lt p\lt 1 . 

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2. Drinfeld’s Lemma for F -isocrystals, I

   https://doi.org/10.1093/imrn/rnae039  

   Kedlaya, Kiran S (March 2024, International Mathematics Research Notices)

   Abstract We prove that in either the convergent or overconvergent setting, an absolutely irreducible $$F$$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $$p$$, further equipped with actions of the partial Frobenius maps, is an external product of $$F$$-isocrystals over the multiplicands. The corresponding statement for lisse $$\overline{{\mathbb{Q}}}_{\ell }$$-sheaves, for $$\ell \neq p$$ a prime, is a consequence of Drinfeld’s lemma on the fundamental groups of absolute products of schemes in characteristic $$p$$. The latter plays a key role in V. Lafforgue’s approach to the Langlands correspondence for reductive groups with $$\ell $$-adic coefficients; the $$p$$-adic analogue will be considered in subsequent work with Daxin Xu. 

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3. Optimal gap-affine alignment in O ( s ) space

   https://doi.org/10.1093/bioinformatics/btad074  

   Marco-Sola, Santiago; Eizenga, Jordan M; Guarracino, Andrea; Paten, Benedict; Garrison, Erik; Moreto, Miquel (February 2023, Bioinformatics)

   Martelli, Pier Luigi (Ed.)

   Abstract MotivationPairwise sequence alignment remains a fundamental problem in computational biology and bioinformatics. Recent advances in genomics and sequencing technologies demand faster and scalable algorithms that can cope with the ever-increasing sequence lengths. Classical pairwise alignment algorithms based on dynamic programming are strongly limited by quadratic requirements in time and memory. The recently proposed wavefront alignment algorithm (WFA) introduced an efficient algorithm to perform exact gap-affine alignment in O(ns) time, where s is the optimal score and n is the sequence length. Notwithstanding these bounds, WFA’s O(s2) memory requirements become computationally impractical for genome-scale alignments, leading to a need for further improvement. ResultsIn this article, we present the bidirectional WFA algorithm, the first gap-affine algorithm capable of computing optimal alignments in O(s) memory while retaining WFA’s time complexity of O(ns). As a result, this work improves the lowest known memory bound O(n) to compute gap-affine alignments. In practice, our implementation never requires more than a few hundred MBs aligning noisy Oxford Nanopore Technologies reads up to 1 Mbp long while maintaining competitive execution times. Availability and implementationAll code is publicly available at https://github.com/smarco/BiWFA-paper. Supplementary informationSupplementary data are available at Bioinformatics online. 

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4. Paludicola gen. nov. and Revision of the Species Formerly in Batrachospermum Section  Turfosa (Batrachospermales, Rhodophyta)

   https://doi.org/10.1111/jpy.13001  

   Vis, Morgan L.; Lee, Janina; Eloranta, Pertti; Chapuis, Iara S.; Lam, Daryl W.; Necchi, Orlando (April 2020, Journal of Phycology)

   Since the first phylogenetic study of the order Batrachospermales, Batrachospermum was shown to be paraphyletic. Subsequently, sections of the genus have been methodically investigated using DNA sequences and morphology in order to propose new genera and delineate species. Batrachospermum section Turfosa is the last section with multiple species yet to be examined. New sequence data of specimens from Europe and the United States were combined with the sparse sequence data already available. Phylogenetic analyses using rbcL and COI- 5P sequences showed this section to be a wellsupported clade, distinct from Batrachospermum section Batrachospermum and its segregate genera. Section Turfosa is raised to the generic rank as Paludicola gen. nov. Substantial genetic variation within the genus was discovered and 12 species are recognized based on DNA sequence data as well as morphological characters and geographic distribution. The following morphological characters were applied to distinguish species: branching pattern (pseudodichotomous or irregular), whorl size (reduced or well developed), primary fascicles (curved or straight), spermatangia origin (primary or secondary fascicles), and carposporophyte arrangement (loose or dense). Previously published species were transferred to the new genus: P. turfosa, P. keratophyta, P. orthosticha, P. phangiae, and P. periploca. Seven new species are proposed as follows: P. groenbladii from Europe; P. communis, P. johnhallii, and P. leafensis from North America; and P. aquanigra, P. diamantinensis, and P. turfosiformis from Brazil. In addition, three unsequenced species in the section, P. bakarensis, P. gombakensis, and P. tapirensis, were transferred to the new genus. 

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5. The R -Process Alliance: Analysis of limited- r stars

   https://doi.org/10.1051/0004-6361/202449376  

   Xylakis-Dornbusch, T; Hansen, T T; Beers, T C; Christlieb, N; Ezzeddine, R; Frebel, A; Holmbeck, E; Placco, V M; Roederer, I U; Sakari, C M; et al (August 2024, Astronomy & Astrophysics)

   Context.In recent years, theR-Process Alliance (RPA) has conducted a successful search for stars that are enhanced in elements produced by the rapid neutron-capture (r-)process. In particular, the RPA has uncovered a number of stars that are strongly enriched in lightr-process elements, such as Sr, Y, and Zr. These so-called limited-rstars were investigated to explore the astrophysical production site(s) of these elements. Aims.We investigate the possible formation sites for light neutron-capture elements by deriving detailed abundances for neutron-capture elements from high-resolution spectra with a high signal-to-noise ratio of three limited-rstars. Methods.We conducted a kinematic analysis and a 1D local thermodynamic equilibrium spectroscopic abundance analysis of three stars. Furthermore, we calculated the lanthanide mass fraction (X_La) of our stars and of limited-rstars from the literature. Results.We found that the abundance pattern of neutron-capture elements of limited-rstars behaves differently depending on their [Ba/Eu] ratios, and we suggest that this should be taken into account in future investigations of their abundances. Furthermore, we found that theX_Laof limited-rstars is lower than that of the kilonova AT2017gfo. The latter seems to be in the transition zone between limited-rX_Laand that ofr-I andr-II stars. Finally, we found that unliker-I andr-II stars, the current sample of limited-rstars is largely born in the Galaxy and is not accreted. 

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